b
\(F =200 N \quad\) for \(0 \leq x \leq 15\)

\(=200-\frac{100}{15}( x -15)\) for \(15 \leq x <30\)

\(W =\int F dx\)

\(=\int_{0}^{15} 200 dx +\int_{15}^{30}\left(300-\frac{100}{15} x \right) dx\)

\(=200 \times 15+300 \times 15-\frac{100}{15} \times \frac{\left(30^{2}-15^{2}\right)}{2}\)

\(=3000+4500-2250\)

\(=5250 J\)